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    $\begingroup$ How can you hate polynomials? What a strange attitude. $\endgroup$ Commented Oct 5, 2011 at 3:25
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    $\begingroup$ Seriously, if you hate polynomials, you hate mathematics. I believe the only reason someone in mathematics can seriously hate polynomials is if his only experience with polynomials comes from artifical math-contest problems (unfortunately, almost all polynomial problems from math contests are extremely artificial and boring). Most of quantitative (= containing actual equality-type results) mathematics is about polynomials in one way or another; for example, characteristic classes theory has lots of them. Isn't that your friend's algebraic topology? $\endgroup$ Commented Oct 5, 2011 at 3:45
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    $\begingroup$ You can lead a horse to water, but you can't make it drink... $\endgroup$ Commented Oct 5, 2011 at 4:07
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    $\begingroup$ Your friend is young, he'll grow up. $\endgroup$ Commented Oct 5, 2011 at 6:22
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    $\begingroup$ Dori, I am embarrassed to admit that I also once 'hated polynomials', and even had the same attitude towards algebraic geometry because that was what it appeared to be about to me at first glance. But now I blame it on mostly being ignorant of the ubiquity of polynomials in mathematics. So like your friend, I was interested in non-commutative geometry and was really enamored with Gel`fand duality - and when I found out that one of the points of view of algebraic geometry is that rings are all viewed as being functions over their spectrum, my attitude immediately changed because of the $\endgroup$ Commented Oct 5, 2011 at 14:58